Internal problem ID [8675]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1095.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime \prime } x +y^{\prime }+l x y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.003 (sec). Leaf size: 23
dsolve(x*diff(diff(y(x),x),x)+diff(y(x),x)+l*x*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} \BesselJ \left (0, \sqrt {l}\, x \right )+c_{2} \BesselY \left (0, \sqrt {l}\, x \right ) \]
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 30
DSolve[l*x*y[x] + y'[x] + x*y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 J_0\left (\sqrt {l} x\right )+c_2 Y_0\left (\sqrt {l} x\right ) \\ \end{align*}